The ruler in the photo helps at least somewhat, but we need precise measurements to give more-specific identification. The bullet is a civil war era yankee .54 or .58-caliber 3-groove Minie-ball. The twist-marks on its top mean that it has been "pulled" out of the muzzleloading rifle's barrel by using a bulletworm attached to the end of the rifle's ramrod. Here's a photo showing what that looked like. (But note, one of the corkscrew-shaped arms of the bulletworm in the photo is broken off.)
Muzzleloading guns sometimes needed to be unloaded, such as when the gunpowder got wet, or you returned to camp from guard duty with a loaded gun. With a muzzleloader gun, you can't simply open up the back end of the barrel to remove the bullet. So, you would attach a bulletworm (also called a bullet-puller) onto the gun's ramrod, insert the ramrod down the gun's barrel, and twist the ramrod until the bulletworm digs into the soft lead bullet's nose, gripping it. Then pull it out of the barrel.
The lead ball on the right in the photo may be a fired pistol-ball. Need precise measurement with a Digital Caliper to be sure.
We also need well-focused closeup photos of the ball and each of the other objects you want us to identify.
